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Description  |
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BACKGROUND OF THE INVENTION
This invention relates generally to the art of laser beam interferometers,
and more particularly to Fizeau heterodyne interferometers.
As is known in the art, heterodyne interferometers in general have a wide
variety of applications. One such application is in laser doppler
velocimeters (LDVs) for radar systems. Heterodyne interferometers of the
Mach-Zehnder type have been utilized successfully in laser doppler
velocimeters. As is known, the local oscillator (i.e. reference) beam
travels along a separate path from the beam transmitted to the target and
the target-reflected return beam in a Mach-Zehnder heterodyne
interferometer. The target return beam and the reference beam are combined
in a recombining beamsplitter and directed onto an optical detector. Such
interferometer is thus a relatively large device and hence may be
unsuitable for applications wherein size is of primary importance. One
possible substitution is the Fizeau heterodyne interferometer, a device
wherein the target-reflected return beam, and the local oscillator (i.e.
reference) beam travel along a common optical path to an optical detector,
thus achieving a compact structure.
In a conventional Fizeau heterodyne interferometer the local oscillator
beam power is fixed at approximately the product of the power of the laser
beam and the reflectivity of a beamsplitter which reflects the laser beam
to produce the local oscillator beam. The operation of the optical
detector is a function of the power of the local oscillator beam which
illuminates the detector. If the local oscillator beam power is too high
the optical detector will not function optimally, resulting in reduced
interferometer signal-to-noise ratio and a corresponding marked decrease
in LDV performance. Additionally, the optimum operating power may vary
from detector to detector. One way of reducing the local oscillator beam
power is to utilize a very low reflectivity beamsplitter to reflect the
laser beam and produce the local oscillator beam. However, repeatable
production of such very low reflectivity beamsplitters is unreliable since
the reflectivity thereof typically varies from beamsplitter to
beamsplitter. Another method of decreasing local oscillator beam power is
to place an optical attenuator in the path of the local oscillator beam.
However, since the local oscillator beam travels along a common path with
the target reflected return beam in a Fizeau interferometer, the optical
attenuator would also weaken the target-reflected return beam, thus
reducing the sensitivity of the interferometer.
SUMMARY OF THE INVENTION
In accordance with the present invention apparatus is provided including
means for producing a beam of energy along a predetermined path. Means
disposed in the predetermined path transmit a first portion of the
produced beam to a target and reflect a second portion of the produced
beam. Means are further included for directing a target-reflected portion
of the transmitted first beam portion and the reflected second beam
portion along a common path to a detector with the reflected second beam
portion being attenuated along the common path and the target-reflected
portion of the transmitted first beam portion being substantially
unattenuated along the common path. The directing means may comprise means
for polarizing the reflected second beam portion as a pair of polarization
components along the common path and for polarizing the target-reflected
portion of the transmitted first beam portion as substantially only the
second one of the pair of polarization components along the common path.
The directing means may further comprise means for selectively coupling to
the detector substantially only the second one of the pair of polarization
components of the reflected second beam portion and the target-reflected
portion of the transmitted first beam portion polarized as the second
polarization component.
Such apparatus may be used in an interferometer, with the second one of the
pair of polarization components of the reflected second beam portion
serving as the local oscillator, or reference, beam for the
interferometer. Thus, the apparatus of the present invention provides an
interferometer having an attenuated local oscillator beam and an
unattenuated target-reflected return beam travelling along a common path
to a detector.
In a preferred embodiment of the present invention, means are provided for
producing a beam of energy along a predetermined path. First and second
waveplates are serially disposed with the beam producing means in the
predetermined path, with a beamsplitter being disposed therebetween in the
predetermined path. A polarization analyzer is disposed in the
predetermined path between the beam producing means and the first
waveplate. With such apparatus an interferometer may be provided wherein
the produced beam is P-polarized and a first portion of the produced beam
couples through the first waveplate, the beamsplitter and the second
waveplate, and wherein the first waveplate and the second waveplate alter
the polarization of the first portion of the produced beam coupled through
the first waveplate, the beamsplitter and the second waveplate to
substantially circular polarization. The apparatus is disposed so that a
substantially circularly polarized return beam couples through the second
waveplate, the beamsplitter and the first waveplate and is incident on the
polarization analyzer, the first and second waveplates altering the
polarization of the return beam coupled therethrough to substantially
S-polarization. The polarization analyzer directs to a detector
substantially the entire S-polarized return beam incident thereon.
Additionally, a second portion of the P-polarized produced beam couples
through the first waveplate, reflects from the beamsplitter and recouples
through the first waveplate and is incident on the polarization analyzer,
the first waveplate changing the polarization of the second beam portion
incident on the polarization analyzer to both P- and S-polarization
components. The polarization analyzer directs to the detector
substantially only the S-polarization component of the second beam portion
incident on the polarization analyzer.
The present invention further provides a method of transmitting a
circularly polarized beam of energy to a target. A P-polarized beam of
energy is produced and directed along a predetermined path. The
polarization of such beam is changed a first predetermined amount to
produce an elliptically polarized intermediate beam having S- and
P-polarization components. The polarization of the intermediate beam is
changed a second predetermined amount to produce a circularly polarized
beam, which is then transmitted to the target. Additionally, the
polarization of the intermediate beam is changed by the first
predetermined amount to produce a reference beam having S- and
P-polarization components. Substantially only the S-polarization component
of the reference beam is directed to a detector. Therefore, the reference
beam is attenuated. Further, the polarization of the circularly polarized
beam reflected by the target is changed by the first and second
predetermined amounts to produce a substantially entirely S-polarized
beam. Substantially only the S-polarized component of such substantially
entirely S-polarized beam is directed to the detector. Thus, the
target-reflected beam is substantially unattenuated.
BRIEF DESCRIPTION OF THE DRAWING
The foregoing features of the present invention and the advantages thereof
may be more fully understood from the following detailed description when
read in conjunction with the accompanying FIGURE, which is a schematic and
block diagram of the improved interferometer of the present invention.
DESCRIPTION OF THE PREFERRED EMBODIMENT
Referring to the FIGURE, shown is the improved Fizeau interferometer 10 of
the present invention used in a laser doppler velocimeter (LDV).
Interferometer 10 is shown to comprise laser portion 12, Brewster plate
14, first and second quarter-waveplates 16, 18, and beamsplitter 20. An
LDV is constructed using interferometer 10 by including optical detector
22 and utilization device 24, as shown. It is noted that certain
conventional appurtenances to such an LDV, for example, power supplies and
telescoping arrangements to define or deflect the beam, have been omitted
for the sake of clarity. The laser here contemplated is a conventional
device comprising laser cell 26 and exciter 28. Laser cell 26 is here a
CO.sub.2 laser and is operated in the CW mode. Fully reflective mirror 30
and partially transmissive mirror 32 define the optical resonator of laser
12. Brewster plate 14 is likewise a conventional device, utilized as a
polarization analyzer in a manner to be described. Thus, a thin-film
polarizer or wire-grid polarizer may be substituted therefor. Conventional
beamsplitter 20 has front face 21 thereof designed with a predetermined,
small reflectivity R of, here, 0.001, for purposes to be described
hereinafter. Suffice it to say here, however, that beamsplitter 20
reflects a small portion of the beam incident thereon from laser 12 to
provide a local oscillator (LO) beam, such LO beam being heterodyned at
optical detector 22 with reflected returns from targets, such as target T.
Optical detector 22 is a conventional photovoltaic or photoconductive
device which produces electrical output signals in response to optical
signals incident thereon. In the present invention, such electrical
signals are fed to utilization device 24, wherein such electrical signals
are conventionally amplified, filtered and processed.
In operation, exciter 28 responds to conventional actuation to electrically
excite the gaseous medium of laser cell 26. Laser transitions occur,
thereby activating the optical resonator formed by mirrors 30, 32, and a
coherent beam of energy is emitted from laser 12 along optical path 34.
The FIGURE depicts this beam as a combination dashed and dotted line. In
the preferred embodiment, laser cell 26 is equipped with Brewster windows
25, 27, forcing the beam of energy emitted from laser 12 to be strongly
P-polarized. The emitted laser beam is incident on first surface 13 of
Brewster plate 14 at the Brewster angle. As stated, Brewster plate 14
functions as a polarization analyzer, here coupling therethrough
substantially only P-polarized components of the laser beam incident
thereon. Any S-polarized components of such beam are reflected by Brewster
plate 14. Thus, any spurious S-polarization present in the laser beam
emitted by laser 12 is reflected by Brewster plate 14 along optical path
36 at an angle to optical path 34. Since, as previously stated, Brewster
windows 25, 27 strongly P-polarize the laser beam emitted by laser 12,
substantially all of such beam is coupled through Brewster plate 14 to
optical path 38. It is seen from the FIGURE that optical path 38 is
substantially parallel to optical path 34, but displaced therefrom by a
small amount due to the passage of the emitted laser beam through Brewster
plate 14. The emitted laser beam coupled to optical path 38 passes through
first quarter-waveplate 16, beamsplitter 20 and second quarter-waveplate
18 in a manner and for purposes to be described. Briefly, however, such
beam after traversing first and second quarter-waveplates 16, 18 and
beamsplitter 20 is transmitted towards a target T for reflection back to
interferometer 10 along optical path 38. The FIGURE illustrates the
transmitted and target reflected beams separately for the sake of clarity,
although it is understood that such beams travel coaxially along optical
path 38. The target-reflected return beam, represented in the FIGURE by a
dashed line, is coupled through second quarter-waveplate 18, beamsplitter
20 and first quarter-waveplate 16 and impinges on second surface 15 of
Brewster plate 14 at the Brewster angle. As will be described in detail
hereinafter, a predetermined portion of the reflected return beam--the
portion which is S-polarized--is reflected by Brewster plate 14 along
optical path 40 at an angle to optical path 38 and is incident on optical
detector 22. The reflected return beam incident on optical detector 22
contains frequency information relating to the doppler velocity of target
T that can be easily retrieved by heterodyning such beam with a local
oscillator beam derived from a portion of the laser beam emitted by laser
12. As discussed, the local oscillator beam is here produced by
beamsplitter 20. The beam emitted from laser 12, coupled through first
quarter-waveplate 16, is incident on front face 21 of beamsplitter 20. A
predetermined, small portion of such incident beam is reflected by front
face 21 back along optical path 38, through first quarter-waveplate 16, to
Brewster plate 14. The beamsplitter-reflected beam is shown as a dotted
line in the FIGURE. For the sake of clarity, the FIGURE shows the
beamsplitter-reflected beam, the beam emitted from laser 12, and the
target-reflected return beam separately; however, it is understood that
all three beams travel coaxially along optical path 38. As will be
described in detail hereinafter, a predetermined portion of the beam
reflected by beamsplitter 20 is S-polarized due to the double-passage of
the beam through first quarter-waveplate 16. This S-polarized portion is
reflected as described by Brewster plate 14 along optical path 40 to
optical detector 22 coaxially with the S-polarized portion of the
target-reflected return beam, although the FIGURE depicts the two beams
separately for convenience. The S-polarized portion of the
beamsplitter-reflected beam is utilized as the LO beam for the
interferometer.
The crystalline optic axes (i.e., the "fast" and "slow" axes) of a
quarter-waveplate are orthogonal to each other. Systems of the prior art
utilize a single quarter-waveplate disposed between a polarization
analyzer (Brewster plate) and a beamsplitter, the quarter-waveplate being
aligned to place its crystal axes at 45.degree. angles to the
P-polarization of the beam emitted from the laser through the Brewster
plate. The P-polarized beam of energy incident on the quarter-waveplate is
coupled therethrough with substantially no loss and is rendered fully
circularly polarized. Such beam is incident on the beamsplitter and upon
reflection remains fully circularly polarized. The beam then passes
through the quarter-waveplate with substantially no loss and has its
circular polarization converted fully to S-polarization by the
quarter-waveplate. Thus, such beam is substantially entirely reflected by
the Brewster plate to the optical detector and becomes the system's LO
beam. A little thought reveals that the power of such LO beam essentially
is the product of the beam emitted by the laser and the reflectivity of
the beamsplitter. It is seen that such power level is basically
non-adjustable, save varying laser power or beamsplitter reflectivity.
Moreover, for lasers of useful power and beamsplitters having reliably
producible reflectivities, the power of the LO beam thus generated is
normally an order of magnitude above the optimum operating power (i.e.
optical bias) level of the optical detector. Thus, the detector operates
inefficiently, resulting in poor LDV signal-to-noise ratio. Further, the
optimum optical bias level varies from detector to detector. Thus,
replacement of a detector due to breakdown, etc., may result in improved
or degraded LDV operation, depending on the optimum optical bias level of
the replacement detector compared with that of the previous detector.
The interferometer of the present invention solves these problems by
producing an LO (reference) beam having a power level which is not simply
the product of the emitted laser beam power and the beamsplitter
reflectivity, but is rather attenuated to a predetermined factor thereof
selected to be within the optimum operating range of optical detector 22.
The power level of such LO beam is also adjustable, allowing replacement
detectors to be optically biased within their individual optimum ranges.
LO beam power attenuation and adjustment is achieved in the present
invention by selectively aligning the crystalline optic axes (i.e., the
"fast" and the "slow" axes) of first quarter-waveplate 16 relative to the
P-polarization of the beam incident thereon from laser 12 via Brewster
plate 14. As discussed, alignment of the crystalline optic axes at
45.degree. angles to the P-polarization of the incident beam produces a
beam which is fully S-polarized upon passage through first
quarter-waveplate 16, reflection from beamsplitter 20, and repassage
through first quarter-waveplate 16. Thus, the entire reflected beam
incident on Brewster plate 14 is reflected by Brewster plate 14 along
optical path 40 and illuminates optical detector 22, providing maximum LO
power. On the other hand, by rotating first quarter-waveplate 16 to align
either of its crystalline optic axes with the P-polarization of the
emitted beam from laser 12, it is seen that the beam's polarization will
be unchanged upon passage through first quarter-waveplate 16. Thus, the
portion of the beam that repasses through first quarter-waveplate 16 after
reflection by beamsplitter 20 remains substantially fully P-polarized.
Hence, practically none of such beam is reflected by Brewster plate 14
along path 40 to optical detector 22; rather, substantially all of such
beam is coupled through Brewster plate 14 to laser 12 via optical path 34.
Thus, optical detector 22 is illuminated with essentially zero LO power. A
little thought therefore reveals that by rotating first quarter-waveplate
16 to place one of its orthogonal crystalline optic axes at a
predetermined angle between 0.degree. and 45.degree. relative to the
P-polarization of the beam emitted from laser 12, the beam reflected by
beamsplitter 20 will comprise both an S-polarized component and a
P-polarized component upon repassage through first quarter-waveplate 16.
As stated, only the S-polarized component is reflected by Brewster plate
14 along optical path 40 to become the LO beam for optical detector 22.
Thus, first quarter-waveplate 16 is rotated to adjust the degree of
S-polarization of such beam and thereby selectively attenuate and adjust
the power of the LO beam illuminating optical detector 22 to be within the
optimum operating power range of the detector.
It is desired that the P-polarized beam emitted by laser 12 be converted to
a fully circularly polarized beam before transmission for reflection by a
target, such as target T, since the target-reflected return beam incident
on Brewster plate 14 will thereby be fully S-polarized and will be
substantially entirely directed to optical detector 22 with essentially
none of such beam coupled to laser 12 and lost to detector 22. However, as
an inherent consequence of aligning the crystalline optic axes of first
quarter-waveplate 16 at other than 45.degree. to the incident
P-polarization of the beam emitted by laser 12, the beam coupled through
first quarter-waveplate 16 and beamsplitter 20 for transmission to target
T is elliptically polarized rather than fully circularly polarized. An
elliptically polarized beam reflected by target T will not be fully
S-polarized upon return through quarter-waveplates 16, 18. Thus, part of
such return beam will be coupled to laser 12 rather than to detector 22 by
Brewster plate 14. The power of the target-reflected return beam available
to detector 22 will thus be reduced, resulting in a corresponding decrease
in the maximum range at which the interferometer can detect target T.
Thus, in the present invention, second quarter-waveplate 18 is provided
having its crystalline optic axes aligned to adjust the elliptical
polarization of the beam incident thereon from beamsplitter 20 to be
substantially fully circular after passage through second
quarter-waveplate 18. Such fully circularly polarized beam, upon
reflection from a target, such as target T, is converted to a fully
S-polarized beam by quarter-waveplates 16, 18. Thus, substantially all of
the target-reflected return beam is directed by Brewster plate 14 to
detector 22, with essentially none of such beam lost by being coupled
through Brewster plate 14 to laser 12.
The precise angle to which first quarter-waveplate 16 is rotated may be
calculated by using the normalized Jones Vector to represent the
P-polarized beam emitted by laser 12 and by representing the optical
elements of interferometer 10 by Jones Matrices. The use of the Jones
Vector and Jones Matrices in determining the effect of optical elements on
a polarized wave is aptly discussed in Introduction to Modern Optics, by
Grant R. Fowles, published by Holt, Reinhart and Winston, Inc., 1975,
section 2.5, pages 33-38. The P-polarized beam emitted by laser 12 and
coupled through Brewster plate 14 may be represented by the following
normalized Jones Vector, and is hereinafter referred to as the input
vector:
##EQU1##
The Jones Matrices for the optical components of interest-- first
quarter-waveplate 16, beamsplitter 20 and second quarter-waveplate 18--are
as follows:
##EQU2##
where R is the reflectivity of front face 21 of beamsplitter 20 (here,
0.001), i=.sqroot.-1, angle "a" is the angle between the P-polarized input
vector, E.sub.i, and a selected one of the crystalline optic axes of first
quarter-waveplate 16 (i.e., the rotation angle of first quarter-waveplate
16), and angle "b" is the angle between the P-polarized input vector,
E.sub.i, and a selected one of the crystalline optic axes of second
quarter-waveplate 18 (i.e., the rotation angle of second quarter-waveplate
18). For the purposes of these calculations, angles "a" and "b" are each
measured with reference to the "slow" axes of first and second
quarterwaveplates 16, 18, respectively. Of course, these calculations
could also be made with respect to the "fast" axes of first and second
quarter-waveplates 16, 18. Additionally, target T may be considered as
having unit reflectivity, thus having the following Jones Matrix:
##EQU3##
Using the above Jones Vector and Matrices representations, it is seen that
the beam emitted by laser 12, after a first transit through first
quarter-waveplate 16, reflection from front face 21 of beamsplitter 20,
and a second transit through first quarter-waveplate 16, is converted to a
beam having the following Jones Vector representation:
##EQU4##
Using basic matrix calculus, the above expression for EHD BR is reduced
to:
##EQU5##
where -cos 2a represents the portion of E.sub.BR which is P-polarized, and
sin 2a denotes the S-polarized component of E.sub.BR.
As is known, the power carried by a wave can be expressed as the vector
representation of the wave multiplied by the complex conjugate of such
vector representation. Thus, the power of wave E.sub.BR is:
##EQU6##
Since the square of the wave amplitude, E.sub.o.sup.2, is proportional to
the power of the beam of energy emitted by laser 12 and coupled through
Brewster plate 14, the above equation may be expressed as:
##EQU7##
where P.sub.o is the output power of laser 12. It is noted that beam
P.sub.BR has a P-polarized power component, P.sub.BRP, and an S-polarized
power component, P.sub.BRS, as follows:
P.sub.BRP .apprxeq.P.sub.o R cos.sup.2 2a (3)
P.sub.BRS .apprxeq.P.sub.o R sin.sup.2 2a (4)
As previously discussed, the beam represented as P.sub.R is incident on
second surface 15 of Brewster plate 14 at the Brewster angle. Thus,
substantially the entire P-polarized component, P.sub.BRP, of beam
P.sub.BR is transmitted through Brewster plate 14 along optical path 34
and coupled into laser 12. Such beam component is shown separately from
the beam emitted by laser 12. It is understood, however, that the two
beams travel coaxially along optical path 34. The S-polarized component,
P.sub.BRS, of beam P.sub.BR is reflected by Brewster plate 14 along
optical path 40 to optical detector 22 and becomes the LO beam for the
interferometer. Thus, equation (4) can be expressed as:
P.sub.BRS .apprxeq.P.sub.o R sin.sup.2 2a.apprxeq.P.sub.LO (4a)
It is noted here that Brewster plate 14 is not an ideal device. Thus, a
small portion, such as 1%, of P-polarized component P.sub.BRP will be
reflected by Brewster plate 14 to optical detector 22, thereby slightly
increasing LO beam power. As will be shown, this causes a slight
degradation in the system's signal-to-noise ratio. However, for purposes
of these calculations, this unwanted P-polarization reflection will be
ignored. With Equation 4a in mind, a little thought reveals that the power
of the LO beam, P.sub.LO, is essentially determined by the output power of
laser 12, the reflectivity of front face 21 of beamsplitter 20, and the
sine of the angle between a crystalline optic axis (here, the slow axis)
of first quarter-waveplate 16 and the P-polarization of input vector
E.sub.i. LO power may be selectively adjusted by varying such angle,
without having to vary either laser output power or beamsplitter
reflectivity.
As previously discussed, when the angle "a" of first quarter-waveplate 16
is changed from 45.degree., the beam coupled through beamsplitter 20 for
transmission to target T is elliptically, rather than fully circularly,
polarized. Thus, second quarter-waveplate 18 is disposed in optical path
38 to compensate for such elliptical polarization and ensure that a
substantially fully circularly polarized beam is transmitted for
reflection by target T. It is manifest that rotation angle "b" between a
selected one of the crystalline optic axes of second quarter-waveplate 18
(here, the "slow" axis) and the P-polarization of input vector E.sub.i be
chosen with rotation angle "a" of first quarter-waveplate 16 in mind.
Referring to the FIGURE, it is seen that the beam emitted from laser 12
through Brewster plate 14 is coupled through first quarter-waveplate 16,
beamsplitter 20 and second quarter-waveplate 18 before striking target T.
The portion of such beam reflected by target T traverses second
quarter-waveplate 18, beamsplitter 20 and first quarter-waveplate 16
before impinging at the Brewster angle on second surface 15 of Brester
plate 14. Assuming beamsplitter 20 has no polarization effects, and
neglecting the loss due to the small reflectivity (typically, 0.001) of
the beamsplitter, the target-reflected return beam at this point is
represented by:
##EQU8##
The power of the target-reflected return beam at this point is:
##EQU9##
It is noted that beam P.sub.TR has a P-polarized power component,
P.sub.TRP, and an S-polarized power component, P.sub.TRS, as follows:
##EQU10##
As noted above, the target-reflected return beam represented as P.sub.TR is
incident on Brewster plate 14 at the Brewster angle. Thus, substantially
all of P-polarized component P.sub.TRP of such beam couples through
Brewster plate 14 and into laser 12 along optical path 34. Brewster plate
14 reflects S-polarized component P.sub.TRS to optical detector 22, via
optical path 40, where such S-polarized component is heterodyned with the
LO beam, P.sub.LO, to produce an electrical target doppler signal. The
target doppler signal is fed to utilization device 24 for amplification,
filtering and processing.
Since reflected return signals from targets such as target T are relatively
weak, it is apparent that for efficient interferometer operation, such
signals must be coupled to optical detector 22 with as little loss as
possible in the interferometer. It follows, therefore, that rotation angle
"b" of second quarter-waveplate 18 is adjusted to maximize the S-polarized
power component, P.sub.TRS, of target-reflected return beam P.sub.TR,
since Brewster plate 14 reflects essentially only S-polarized components
to optical detector 22. From Equation 5, it is seen that the S-polarized
component of E.sub.TR is:
##EQU11##
By taking the first derivative of Equation 9 with respect to "b" and
setting such derivative equal to zero, the minima and maxima of the
S-polarization component, E.sub.TRS, are found to exist where:
##EQU12##
Therefore, by inserting into Equation 10 the rotation angle "a" obtained
from Equation 4a for optimum LO power, rotation angle "b" can be
calculated and second quarter-waveplate 18 rotated thereto to maximize the
power of the target-reflected return beam illuminating optical detector
22. Optimum interferometer sensitivity and efficiency is thereby achieved.
In the interferometer of the preferred embodiment, laser 12 emits a beam
having a power P.sub.o of 5 Watts (W). Brewster windows 25, 27 are
selected to provide such beam with a P-polarization purity of >1000:1.
Brewster plate 14 provides an S/P discrimination ratio of about 100:1,
thus coupling essentially the full 5 W of beam power therethrough to
optical path 38. As stated, front face 21 of beamsplitter 20 has a
reflectivity, R=0.001. Here, optical detector 22 has an optimum LO
(optical bias) power of 0.5 mW. As discussed, the optimum optical bias
power typically differs from detector to detector. In practice, the first
step is to set LO beam power to the optimum level for the optical detector
used. From Equation 2 it is seen that the power, P.sub.BR, of the beam
reflected by beamsplitter 20 and incident on second surface 15 of Brewster
plate 14 is:
##EQU13##
Equation 4 reveals that, theoretically, LO beam power P.sub.LO is (5
mW)sin.sup.2 2a; however, since Brewster plate 14 has a finite S/P
discrimination ratio of, here, 100:1, it is seen that 1% of the
P-polarized component (cos.sup.2 2a) of P.sub.BR is reflected by Brewster
plate 14 along optical path 40. Hence, the actual LO power delivered to
optical detector 22 is:
P.sub.LO '=P.sub.BRS +(0.01)P.sub.BRP
P.sub.LO '=(5 mW)sin.sup.2 2a+(0.01)(5 mW)cos.sup.2 2a (11)
0.5 mW=(5 mW)sin.sup.2 2a+(0.05 mW)cos.sup.2 2a
Thus, it is seen that first quarter-waveplate 16 rotation angle "a" must be
set to approximately 9.degree. to achieve a total LO power of 0.5 mW. In
system operation, first quarter-waveplate 16 is rotated to a 9.degree.
rotation angle and LO beam power is observed at optical detector 22. The
rotation of first quarter-waveplate 16 is slightly adjusted, if necessary,
to obtain precisely 0.5 mW of LO beam power. Unfortunately, Equation 11
shows that the LO beam includes a P-polarization power component of 0.045
mW, introducing about 0.4 dB of noise at optical detector 22. However,
this slight noise presence is more than offset by the increase in detector
efficiency resulting from decreasing the LO power from 5 mW (P.sub.o xR)
to 0.5 mW--the optimum operating power for this detector.
Having set first quarter-waveplate 16 to achieve the optimum LO beam power
for optical detector 22, second quarter-waveplate 18 is rotated to its
proper rotation angle. That is, second quarter-waveplate 18 is rotated to
transmit to target T a beam which is substantially circularly polarized.
In operation, this is done simply by adjusting the rotation of second
quarter-waveplate 18 to maximize the power of the target-reflected return
beam illuminating optical detector 22. To put it another way, second
quarter-waveplate 18 is rotated to peak the S-polarized component of the
target-reflected return beam incident on Brewster plate 14, thus implying
that the beam transmitted to target T is maximally circularly polarized.
Rotation angle "b" may be calculated simply by using Equation 10 with the
rotation angle a obtained from Equation 11. In the system of the preferred
embodiment, with a=9.degree., rotation angle "b" must be approximately
143.degree.. Inserting the calculated values of "a" and "b" into Equation
6, the target-reflected return beam incident on Brewster plate 14 is:
##EQU14##
Thus, such beam is not fully S-polarized; rather, a small (0.097) relative
P-polarization component is present. This implies that the polarization of
the beam transmitted to target T is not completely circular, but is
instead slightly elliptical. Such P-polarization component is coupled by
Brewster plate 14 along optical path 34 into laser 12, resulting in a
slight (0.45 dB) loss of power as compared with a system that transmits a
fully circularly-polarized beam to target T. This loss of return beam
power, when taken with the 0.4 dB LO beam P-polarization noise, yields a
total loss of less than 1 dB as a result of the rotation of first and
second quarter-waveplates 16, 18.
Having described a preferred embodiment of the present invention, numerous
modifications may become apparent to those skilled in the art without
departing from the spirit of the invention. For example, the invention is
not restricted to the use of quarter-waveplates to change the polarization
state of a beam of energy; rather, other elements which alter the
polarization state of an incident beam of energy may be substituted
therefor. Also, laser cell 25 need not be a CO.sub.2 laser and may also be
a pulsed, rather than a CW, device. Additionally, laser power is not
limited to 5 W, nor is beamsplitter reflectivity limited to 0.001.
Further, the concepts described need not be applied to a heterodyne
interferometer; rather, the invention may be employed in any Fizeau-type
interferometer in which it is desirable to vary the power of the reference
beam (described above as the LO beam) with respect to the power of the
target beam in order to vary the degree of interference between the two
beams. Accordingly, it is understood that the invention is to be limited
only by the scope of the appended claims.
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